Suppose you are on a game show and there are three closed doors. Behind one door is a car, and behind the other two doors are goats. Choose one door at random. What is the probability that you chose the winning door (the car)? Suppose that after you choose, but before your chosen door is opened, the host opens one of the unchosen doors, revealing a goat. The host then offers you the chance to change your choice to the remaining closed doors. What should you do? If you switch doors after one goat is revealed, does that increase, decrease, or have no effect on your chances? Why? What do you think the probability of winning is if you switch? If you don’t switch?

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